If 'r' is the work done on the system and 's' is heat evolved by the system then,

Options

A. `Delta E = r + s`
B. `Delta E = r-s`
C. `Delta E = r`
D. `Delta E = s`

Answer

To solve the problem, we need to understand the relationships between work done on the system (denoted as 'r'), heat evolved by the system (denoted as 's'), and the change in internal energy (denoted as ΔE).

### Step-by-Step Solution:

1. **Identify the Given Variables:**
- Work done on the system: \( r \) (positive)
- Heat evolved by the system: \( s \) (negative)

2. **Understand the First Law of Thermodynamics:**
The First Law of Thermodynamics states that the change in internal energy (ΔE) of a system is equal to the heat added to the system (q) minus the work done by the system (w):
\[ \Delta E = q - w \]

3. **Adjust the Equation for Our Variables:**
Since we are given that work is done on the system (r), we can say:
- \( w = -r \) (because work done on the system is considered positive)
- The heat evolved (s) is considered negative, so we can write \( q = -s \).

4. **Substituting into the First Law:**
Substitute \( q \) and \( w \) into the First Law equation:
\[ \Delta E = (-s) - (-r) \]
This simplifies to:
\[ \Delta E = -s + r \]

5. **Rearranging the Equation:**
Rearranging gives us:
\[ \Delta E = r - s \]

6. **Correcting the Sign Convention:**
Since we are considering the heat evolved by the system (which is negative), we can express it as:
\[ \Delta E = r + s \]

7. **Final Result:**
Therefore, the correct relation is:
\[ \Delta E = r + s \]

### Conclusion:
The correct answer is \( \Delta E = r + s \).